Data processing: measuring – calibrating – or testing – Measurement system in a specific environment – Electrical signal parameter measurement system
Patent
1995-10-04
1999-01-19
Stamber, Eric W.
Data processing: measuring, calibrating, or testing
Measurement system in a specific environment
Electrical signal parameter measurement system
702 66, 702195, 36472419, G06F 1714
Patent
active
058625160
DESCRIPTION:
BRIEF SUMMARY
TECHNICAL FIELD
The present invention relates to the fields of waveform analysis, waveform synthesis, noise suppression, signal detection and transmission bandwidth compression using computers.
BACKGROUND ART
The Fourier analysis which is well known as FFT (fast Fourier Transformation) is one form of harmonic analysis in which frequencies to be analyzed have a harmonic relationship represented by n/T (n=1, 2, . . . ) where T is the interval of a waveform. Periodgram is a known method for period analysis, however, this requires a waveform of sufficiently longer interval than the period for analysis and cannot attain accuracy unless the periodicity of the waveform is relatively prominent. This is also true of the correlation method. The auto regression model or auto regression moving average (ARMA) model that is used for time series analysis corresponds to a digital lowpass or bandpass filter and requires a waveform of sufficient interval as in the above approaches. Prony's method, which is a form of non-harmonic analysis, cannot make an accurate analysis when noise is present.
SUMMARY OF THE INVENTION
It is an object of the present invention to provide a method of detecting the period and amplitude of sinusoids which are not necessarily harmonic with one period from a waveform of relatively short interval with high accuracy, and a method of synthesizing such waveform.
To solve the above-stated problems, the present invention provides a method for analyzing a physical waveform into non-harmonic frequency components, comprising: (a) converting a given interval of a physical waveform into a corresponding digitized wave data; (b) multiplying said digitized wave data by a first sine and a first cosine function having a first predetermined period, respectively, to provide a first and a second product value; (c) summing said first and second product values over a first predetermined interval, respectively, to provide a first and a second summation value, said first predetermined interval being an integer multiple of said first predetermined period and being equal to or smaller than said given interval; (d) determining the amplitudes of said first sine and first cosine functions based on said first and second summation values, respectively; (e) subtracting from said digitized wave data a sine and a cosine waveform having the thus determined respective amplitudes and said first predetermined period to provide a residual wave data; (f) successively performing the steps (b) to (e) on said digitized wave data using a second to n-th sine and cosine functions having a second to n-th predetermined periods to provide their respective (n-1) residual wave data; (g) checking the power of said n residual wave data to determine as a first non-harmonic frequency component said sine and cosine waveforms providing a minimum residual wave data power; (h) subtracting from said digitized wave data said sine and cosine waveforms providing the minimum residual wave data power to provide a first residual waveform; (i) successively performing the steps (b) to (h) on said first to n-th residual waveforms to determine a second to n-th non-harmonic frequency components. ##EQU1##
The amplitude A(T) of the sine function of the given period T and the amplitude B(T) of the cosine function of the given period T are respectively
Thus, residual wave data R(m) is
The residual amount Q(T) resulting from summing the square of R(m) over a defined interval from J to M is ##EQU2##
Assuming that W(m) is a sine waveform having an amplitude V, a period (T+d) and a phase P and also that L=nT(n=1, 2, 3, . . . ), the A(T) and B(T) are respectively
When d=0, i.e., the given period coincides with the period of a sine waveform of W(m), the Q(T) is the least or the minimum. Accordingly, the amplitude A.sub.1 of the first sine function and the amplitude B.sub.1 of the first cosine function are
Thus, adding the first sine function and the first cosine function results equivalently in the above-mentioned sine waveform having the amplitude V and the phase P. T
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